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We apply the continuum distorted-wave eikonal initial state and theindependent electron model to describe the multiple ionization of Arby He$^{2+}$ and He$^+$ in the energy range 0.1-10 Mev/amu.Auger-like post collisional processes are included, which enhancethe high energy multiple ionization cross sections via ionization ofthe inner shells. All Ar electrons (K, L and M-shells) have beenincluded in these calculations. The results agree well with theexperimental data at high energies, where the post-collisionalionization is the main contribution. At intermediate impact energiesthe description is also good though it tends to overestimate thetriple and quadruple ionization data at intermediate energies. Weanalyze this by comparing the present results for He$^{+2}$ in Ar,with previous ones for He$^{+2}$ in Ne and Kr. It was found that thetheoretical description improves from Ne to Ar and Kr, with thelatter being nicely described even at intermediate energies. Thepresent formalism is also tested for Ar inner shell and totalionization cross sections. In all the cases the results above 0.1MeV/amu are quite reasonable, as compared with the experimental dataavailable and with the ECPSSR values.